Swiss Cottage WA2 (2021+2022) Revision Paper. QP

1MATHEMATICAL FORMULAE1. ALGEBRAQuadratic EquationFor the equation 2axbxc0,242bbacxa.Binomial Theorem12212nnnnnrrnnnn(ab)aabab.....ab....brwhere n is a positive integer and1........1!!!!nnnnrnrnrrr .2. TRIGONOMETRYIdentities22sincos1AA22sec1tanAA22cosec1cotAAsinsincoscossinABABABcoscoscossinsinABABAB∓tantantan1tantanABABAB∓sin22sincosAAA2222cos2cossin2cos112sinAAAAA22tantan21tanAAAFormulae for ABCsinsinsinabcABC2222cosabcbcA1sin2bcA For Examiner’s use23

21It is thought that the selling price of a used car, $P, and the age of that car, m months, can be modelled by lnPamb. When values of P are plotted against lnm, a straight line is obtained. It is given that 112 000P when 11m and that 47 500P when 75m. Find(i)the values of a and of b, [3](ii)the value of m when 90 000P. [2]2Recorded values of yield of corn, y kg/acre, and amount of fertiliser applied, x kg/acre, are shown in the table below.x (kg/acre)4080120160200y (kg/acre)100111119126132It is known that the y and x are related by the equation ybax, where a and b are constants.(i)On graph paper, plot y against x and draw a straight line graph. The vertical y-axis should start at 70 and have a scale of 2 cm to 10. The horizontal x-axis should start at 0 and have a scale of 2 cm to 2.[3]Use your graph to estimate(ii)the yield of corn when no fertiliser is used,[1](iii)the value of a. [2](iv)the expected yield when 100 kg/acre of fertiliser is applied.[2]3Given that 2334f234xxx, find f.x [3]4Find the derivative of the curve 4(23)(3).yxx [3]5Given that 23,43xyx express ddyx in the form 3,43hxxmx where h and m are constants. [4]

3End of Paper